arXiv subjects

Laia Barjuan

Publications and source records attributed to Laia Barjuan.

3 recordsLinked to original sources

arXiv2026

How Rich is the Rich-Club? Super Rich-Club Organization in Complex Networks

The rich-club coefficient is used in complex networks to quantify the tendency of progressively higher-degree nodes to be more densely connected than expected by chance. However, it does not capture whether high degree nodes towards the core are actually more interconnected than the original network. Here, we jointly analyze the rich-club coefficient and an enrichment coefficient, which quantifies whether the internal average degree of progressively higher-degree subgraphs is greater than that of the original network, despite the decreasing number of nodes. We apply this framework to real and synthetic networks. Our results reveal three distinct regimes of core organization: rich-club organization without enrichment, enrichment without rich-club organization, and a combination of both, which we call Super Rich-Club organization. In the latter regime, high-degree nodes form cohesive and unusually dense cores that support efficient communication. Our results show that characterizing core organization across structural scales requires considering both relative density and internal connectivity, revealing a stronger form of core organization in real systems with implications for network structure, spectral properties that govern dynamical processes, and communicability.

physics.soc-ph↗

arXiv2024

The multiscale self-similarity of the weighted human brain connectome

Anatomical connectivity between different regions in the brain can be mapped to a network representation, the connectome, where the intensities of the links, the weights, influence its structural resilience and the functional processes it sustains. Yet, many features associated with the weights in the human brain connectome are not fully understood, particularly their multiscale organization. In this paper, we elucidate the architecture of weights, including weak ties, in multiscale hierarchical human brain connectomes reconstructed from empirical data. Our findings reveal multiscale self-similarity in the weighted statistical properties, including the ordering of weak ties, that remain consistent across the analyzed length scales of every individual and the group representatives. This phenomenon is effectively captured by a renormalization of the weighted structure applied to hyperbolic embeddings of the connectomes, based on a unique weighted geometric model that integrates links of all weights across all length scales. This eliminates the need for separate generative weighted connectivity rules for each scale or to replicate weak and strong ties at specific scales in brain connectomes. The observed symmetry represents a distinct signature of criticality in the weighted connectivity of human brain connectomes, aligning with the fractality observed in their topology, and raises important questions for future research, like the existence of a resolution threshold where the observed symmetry breaks, or whether it is preserved in cases of neurodegenerative disease or psychiatric disorder.

q-bio.NC↗

arXiv2023

Optimal navigability of weighted human brain connectomes in physical space

The architecture of the human connectome supports efficient communication protocols relying either on distances between brain regions or on the intensities of connections. However, none of these protocols combines information about the two or reaches full efficiency. Here, we introduce a continuous spectrum of decentralized routing strategies that combine link weights and the spatial embedding of connectomes to transmit signals. We applied the protocols to individual connectomes in two cohorts, and to cohort archetypes designed to capture weighted connectivity properties. We found that there is an intermediate region, a sweet spot, in which navigation achieves maximum communication efficiency at low transmission cost. Interestingly, this phenomenon is robust and independent of the particular configuration of weights.Our results indicate that the intensity and topology of neural connections and brain geometry interplay to boost communicability, fundamental to support effective responses to external and internal stimuli and the diversity of brain functions.

q-bio.NC↗